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	<id>https://wikisofia.cz/w/index.php?action=history&amp;feed=atom&amp;title=Rasiow%C3%A9-Sikorsk%C3%A9ho_lemma</id>
	<title>Rasiowé-Sikorského lemma - Historie editací</title>
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	<updated>2026-04-20T21:44:54Z</updated>
	<subtitle>Historie editací této stránky</subtitle>
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	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Rasiow%C3%A9-Sikorsk%C3%A9ho_lemma&amp;diff=7221&amp;oldid=prev</id>
		<title>Veronika.Kovrzkova: Veronika Kovrzková (ver.kovrzkova@centrum.cz) přesunul stránku Rasiové-Sikorského lemma na Rasiowé-Sikorského lemma</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Rasiow%C3%A9-Sikorsk%C3%A9ho_lemma&amp;diff=7221&amp;oldid=prev"/>
		<updated>2014-10-25T18:42:46Z</updated>

		<summary type="html">&lt;p&gt;Veronika Kovrzková (ver.kovrzkova@centrum.cz) přesunul stránku &lt;a href=&quot;/wiki/Rasiov%C3%A9-Sikorsk%C3%A9ho_lemma&quot; class=&quot;mw-redirect&quot; title=&quot;Rasiové-Sikorského lemma&quot;&gt;Rasiové-Sikorského lemma&lt;/a&gt; na &lt;a href=&quot;/wiki/Rasiow%C3%A9-Sikorsk%C3%A9ho_lemma&quot; title=&quot;Rasiowé-Sikorského lemma&quot;&gt;Rasiowé-Sikorského lemma&lt;/a&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 25. 10. 2014, 18:42&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-notice&quot; lang=&quot;cs&quot;&gt;&lt;div class=&quot;mw-diff-empty&quot;&gt;(Žádný rozdíl)&lt;/div&gt;
&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;</summary>
		<author><name>Veronika.Kovrzkova</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Rasiow%C3%A9-Sikorsk%C3%A9ho_lemma&amp;diff=7219&amp;oldid=prev</id>
		<title>Veronika.Kovrzkova v 25. 10. 2014, 18:41</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Rasiow%C3%A9-Sikorsk%C3%A9ho_lemma&amp;diff=7219&amp;oldid=prev"/>
		<updated>2014-10-25T18:41:52Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 25. 10. 2014, 18:41&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Řádek 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;Mějme &amp;lt;math&amp;gt;S_{n}\subseteq \mathbb{B}&amp;lt;&lt;/del&gt;/&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;math&amp;gt; takové, že &amp;lt;math&amp;gt;\bigwedge S_{n}&amp;lt;&lt;/del&gt;/&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;math&amp;gt; je definovaná &amp;lt;math&amp;gt;\forall n \in \omega&amp;lt;&lt;/del&gt;/&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;math&amp;gt;. Pak existuje utrafiltr &amp;lt;math&amp;gt;U&amp;lt;&lt;/del&gt;/&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;math&amp;gt; na &amp;lt;math&amp;gt;\mathbb{B}&amp;lt;&lt;/del&gt;/&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;math&amp;gt; takový, že kdykoli &amp;lt;math&amp;gt;S_{n} \subseteq U&amp;lt;&lt;/del&gt;/&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;math&amp;gt;, pak i &amp;lt;math&amp;gt;\bigwedge S_{n} \in U&amp;lt;&lt;/del&gt;/&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;math&amp;gt;&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Lemma pojmenované po polských matematicích [http:&lt;/ins&gt;//&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;en.wikipedia.org&lt;/ins&gt;/&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;wiki&lt;/ins&gt;/&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Helena_Rasiowa Heleně Rasiowé] a [http:&lt;/ins&gt;//&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;en.wikipedia.org&lt;/ins&gt;/&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;wiki/Roman_Sikorski Romanu Sikorském] je jednou z forcingových technik. Důsledkem tohoto lemmatu je '''úplnost predikátové logiky''' pro spočetné jazyky.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Rasiowa-Sikorski lemma se také používá v teorii množin k prokázání existence generických filtrů nad spočetnými strukturami&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;Důsledkem této věty je &lt;/del&gt;'''&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;úplnost predikátové logiky&lt;/del&gt;'''.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;== Znění ==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Mějme &amp;lt;math&amp;gt;S_{n}\subseteq \mathbb{B}&amp;lt;/math&amp;gt; takové, že &amp;lt;math&amp;gt;\bigwedge S_{n}&amp;lt;/math&amp;gt; je definovaná &amp;lt;math&amp;gt;\forall n \in \omega&amp;lt;/math&amp;gt;. Pak existuje ultrafiltr &amp;lt;math&amp;gt;U&amp;lt;/math&amp;gt; na &amp;lt;math&amp;gt;\mathbb{B}&amp;lt;/math&amp;gt; takový, že kdykoli &amp;lt;math&amp;gt;S_{n} \subseteq U&amp;lt;/math&amp;gt;, pak i &amp;lt;math&amp;gt;\bigwedge S_{n} \in U&amp;lt;/math&amp;gt;.&lt;/ins&gt;'''&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;== Zdroj ==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;* MONK J. Donald. Handbook of Boolean algebras: Vol. 1. North-Holland, 1989&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[[Kategorie: Struktury a algebry]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Veronika.Kovrzkova</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Rasiow%C3%A9-Sikorsk%C3%A9ho_lemma&amp;diff=7218&amp;oldid=prev</id>
		<title>Veronika.Kovrzkova v 25. 10. 2014, 16:35</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Rasiow%C3%A9-Sikorsk%C3%A9ho_lemma&amp;diff=7218&amp;oldid=prev"/>
		<updated>2014-10-25T16:35:17Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;tr class=&quot;diff-title&quot; lang=&quot;cs&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Starší verze&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Verze z 25. 10. 2014, 16:35&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Řádek 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Řádek 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Mějme &amp;lt;math&amp;gt;S_{n}\subseteq \mathbb{B}&amp;lt;/math&amp;gt; takové, že &amp;lt;math&amp;gt;\bigwedge S_{n}&amp;lt;/math&amp;gt; je definovaná &amp;lt;math&amp;gt;\forall n \in \omega&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;$&lt;/del&gt;&amp;lt;/math&amp;gt;. Pak existuje utrafiltr &amp;lt;math&amp;gt;U&amp;lt;/math&amp;gt; na &amp;lt;math&amp;gt;\mathbb{B}&amp;lt;/math&amp;gt; takový, že kdykoli &amp;lt;math&amp;gt;S_{n} \subseteq U&amp;lt;/math&amp;gt;, pak i &amp;lt;math&amp;gt;\bigwedge S_{n} \in U&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Mějme &amp;lt;math&amp;gt;S_{n}\subseteq \mathbb{B}&amp;lt;/math&amp;gt; takové, že &amp;lt;math&amp;gt;\bigwedge S_{n}&amp;lt;/math&amp;gt; je definovaná &amp;lt;math&amp;gt;\forall n \in \omega&amp;lt;/math&amp;gt;. Pak existuje utrafiltr &amp;lt;math&amp;gt;U&amp;lt;/math&amp;gt; na &amp;lt;math&amp;gt;\mathbb{B}&amp;lt;/math&amp;gt; takový, že kdykoli &amp;lt;math&amp;gt;S_{n} \subseteq U&amp;lt;/math&amp;gt;, pak i &amp;lt;math&amp;gt;\bigwedge S_{n} \in U&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Důsledkem této věty je '''úplnost predikátové logiky'''.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Důsledkem této věty je '''úplnost predikátové logiky'''.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Veronika.Kovrzkova</name></author>
		
	</entry>
	<entry>
		<id>https://wikisofia.cz/w/index.php?title=Rasiow%C3%A9-Sikorsk%C3%A9ho_lemma&amp;diff=7217&amp;oldid=prev</id>
		<title>Veronika.Kovrzkova: Založena nová stránka s textem „Mějme &lt;math&gt;S_{n}\subseteq \mathbb{B}&lt;/math&gt; takové, že &lt;math&gt;\bigwedge S_{n}&lt;/math&gt; je definovaná &lt;math&gt;\forall n \in \omega$&lt;/math&gt;. Pak existuje utr…“</title>
		<link rel="alternate" type="text/html" href="https://wikisofia.cz/w/index.php?title=Rasiow%C3%A9-Sikorsk%C3%A9ho_lemma&amp;diff=7217&amp;oldid=prev"/>
		<updated>2014-10-25T16:34:27Z</updated>

		<summary type="html">&lt;p&gt;Založena nová stránka s textem „Mějme &amp;lt;math&amp;gt;S_{n}\subseteq \mathbb{B}&amp;lt;/math&amp;gt; takové, že &amp;lt;math&amp;gt;\bigwedge S_{n}&amp;lt;/math&amp;gt; je definovaná &amp;lt;math&amp;gt;\forall n \in \omega$&amp;lt;/math&amp;gt;. Pak existuje utr…“&lt;/p&gt;
&lt;p&gt;&lt;b&gt;Nová stránka&lt;/b&gt;&lt;/p&gt;&lt;div&gt;Mějme &amp;lt;math&amp;gt;S_{n}\subseteq \mathbb{B}&amp;lt;/math&amp;gt; takové, že &amp;lt;math&amp;gt;\bigwedge S_{n}&amp;lt;/math&amp;gt; je definovaná &amp;lt;math&amp;gt;\forall n \in \omega$&amp;lt;/math&amp;gt;. Pak existuje utrafiltr &amp;lt;math&amp;gt;U&amp;lt;/math&amp;gt; na &amp;lt;math&amp;gt;\mathbb{B}&amp;lt;/math&amp;gt; takový, že kdykoli &amp;lt;math&amp;gt;S_{n} \subseteq U&amp;lt;/math&amp;gt;, pak i &amp;lt;math&amp;gt;\bigwedge S_{n} \in U&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Důsledkem této věty je '''úplnost predikátové logiky'''.&lt;/div&gt;</summary>
		<author><name>Veronika.Kovrzkova</name></author>
		
	</entry>
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